lisa and james tuttle moved with children to idyllic geldeston , norfolk .
their dogs kept escaping onto neighbouring farmland .
they were warned if dogs kept bothering farmer 's birds , they 'd be shot .
couple believed dogs were gentle and would n't have attacked birds .
in 2014 while family were on holiday , gamekeeper shot two of the dogs .
acted within law so was not charged .
family are devastated by loss of pets and now want to move .